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U-statistics based on the Green's function of the Laplacian on the circle and the sphere

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  • Pycke, J.-R.

Abstract

We show that the Watson and Cramer-von Mises statistics are related to Green's function of the Laplacian on a circle. A generalization leads to a new U-statistic whose kernel is the Green function of the Laplacian on the sphere.

Suggested Citation

  • Pycke, J.-R., 2007. "U-statistics based on the Green's function of the Laplacian on the circle and the sphere," Statistics & Probability Letters, Elsevier, vol. 77(9), pages 863-872, May.
    • Handle: RePEc:eee:stapro:v:77:y:2007:i:9:p:863-872
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    References listed on IDEAS

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    1. Pycke, Jean-Renaud, 2003. "Multivariate extensions of the Anderson-Darling process," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 387-399, July.
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